OPTIMALITY OF ORTHONORMAL TRANSFORMS FOR SUBBAND CODING

Theory of optimal orthonormal filter banks has recently been d veloped under the assumption that quantizers operate at hig h bit rates. We show that the theory can be simplified if a more gener al model for quantizers is used. With such a model, we show that principal component filter banks (PCFB) are optimal for orth normal subband coding under all bit rates and bit allocation str ategies. This establishes the link between two fundamental problems : principal component representation of signals and optimal orth onormal subband coding. In block transform case, the Karhunen-L oeve transform is a PCFB. At the other extreme, PCFB’s with ideal fi lters have recently been constructed. In the intermediate ca s of FIR orthonormal filter banks, it has recently been shown that t ere does not always exist a PCFB for a given input. This case is addressed in this paper with some new insights.